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A013610","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:   1;\n  1:   9,    36,     36;\n  2:  25,   200,    600,     800,      400;\n  3:  49,   588,   2940,    7840,    11760,     9408,      3136;\n  4:  81,  1296,   9072,   36288,    90720,   145152,    145152,      82944,      20736;\n  5: 121,  2420,  21780,  116160,   406560,   975744,   1626240,    1858560,    1393920,     619520,      123904;\n  6: 169,  4056,  44616,  297440,  1338480,  4283136,   9993984,   17132544,   21415680,   19036160,    11421696,     4153344,      692224;\n  7: 225,  6300,  81900,  655200,  3603600, 14414400,  43243200,   98841600,  172972800,  230630400,   230630400,   167731200,    83865600,    25804800,     3686400;\n  8: 289,  9248, 138720, 1294720,  8415680, 40395264, 148115968,  423188480,  952174080, 1692753920,  2369855488,  2585296896,  2154414080,  1325793280,   568197120,  151519232,   18939904;\n  9: 361, 12996, 220932, 2356608, 17674560, 98977536, 428902656, 1470523392, 4043939328, 8986531840, 16175757312, 23528374272, 27449769984, 25338249216, 18098749440, 9652666368, 3619749888, 851705856, 94633984;\n","recurrence_sentence":"The row polynomials satisfy (4*n^2-4*n+1)*P(n,x) = (4*n^2+4*n+1+(16*n^2+16*n+4)*x+(16*n^2+16*n+4)*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((4*n^2 + 4*n + 1 + (16*n^2 + 16*n + 4)*x + (16*n^2 + 16*n + 4)*x^2)*P[n - 1, x])/(4*n^2 - 4*n + 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = ((4*n^2 + 4*n + 1 + (16*n^2 + 16*n + 4)*x + (16*n^2 + 16*n + 4)*x^2)*v[i - 1])/(4*n^2 - 4*n + 1)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = 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